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Optimal controls for distributed parameter systems with mixed constraints. (English) Zbl 0731.49031

The author establishes a Pontryagin type maximum principle for an optimal control problem with mixed constraints, governed by the semilinear evolution equation \(x'(t)=Ax(t)+f(t,x(t),u(t)),\quad t\in [0,T],\) where A is the infinitesimal generator of a \(C_ 0\)-semigroup on a Banach space and f is strongly measurable in t, Lipschitz continuous in x and continuous in u. The main tool in the present approach is the Ekeland’s variational principle. The notion of Clarke’s generalized gradient is used.
Reviewer: C.Popa (Iaşi)

MSC:

49K27 Optimality conditions for problems in abstract spaces
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